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We introduce the notion of a near left almost ring (abbreviated as nLAring) which is in fact a generalization of left almost ring. A near left almost ring is a nonassociative structure with respect to both the binary operations "+" and ".". However, it possesses properties which we usually encounter in "near ring" and "LAring". Historically, the first step towards the nearrings in axiomatic research was done by Dickson in 1905. He showed that there do exist, "Fields" with only one distributive law" (Nearfields) some year later these nearfields showed up the connection between nearfields and fixedpoint free permutation groups. A couple of years later Veblen and Wedderburn started to use nearfields coordinatize certain kinds of geometric planes.
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